K\"ahler manifolds and mixed curvature
K\"ahler manifolds and mixed curvature
复制标题
DOI：
--
复制
发表时间：
2020-09
期刊：
影响因子：
--
通讯作者：
Jianchun Chu;Man-Chun Lee;Luen-Fai Tam
中科院分区：
文献类型：
--
作者：
Jianchun Chu;Man-Chun Lee;Luen-Fai Tam
.本文考虑了具有非正混合曲率的紧致Küahler流形，它是Ricci曲率和全纯截面曲率的“凸组合”。我们证明在这种情况下，典范线丛是nef。此外，如果曲率在某点为负，则流形是射影的，标准线丛是大的且nef。如果另外曲率是负的，则典范线丛是充分的。作为应用，我们回答了Ni关于具有负k -Ricci曲率的流形的一个问题，并将Wu-Yau和Diverio-Trapani的一个结果推广到共形的Küahler情形.证明了当混合曲率为正时，紧致Küahler流形是单连通的且是射影的.
. In this work we consider compact K¨ahler manifolds with nonpositive mixed curvature which is a “convex combination” of Ricci curvature and holomorphic sectional curvature. We show that in this case, the canonical line bundle is nef. Moreover, if the curvature is negative at some point, then the manifold is projective with canonical line bundle being big and nef. If in addition the curvature is negative, then the canonical line bundle is ample. As an application, we answer a question of Ni concerning manifolds with negative k -Ricci curvature and generalize a result of Wu-Yau and Diverio-Trapani to the conformally K¨ahler case. We also show that the compact K¨ahler manifold is projective and simply connected if the mixed curvature is positive.